Foto Pesquisadores

Mikhail V. Solodov

Office address:
Instituto de Matematica Pura e Aplicada,
Estrada Dona Castorina 110,
Jardim Botânico,
Rio de Janeiro, RJ, CEP 22460-320, Brazil.

Phone: (55-21)-2529-5228.
FAX: (55-21)-2529-5129.
E-mail address: image.


PROFESSIONAL INTERESTS

My research interests lie in the areas of optimization theory and applications, operations research, and related issues in numerical analysis and computational mathematics.

Research Summary

  • Theory and algorithms for solving variational inequality and complementarity problems.
  • Proximal point and related methods.
  • Regularity. Constraint qualifications. Optimality conditions.
  • Perturbation and error-stability analysis of computational algorithms.
  • Parallel optimization algorithms.
  • Applications of optimization to artificial intelligence, especially machine learning.

Editorial Work

Publications

Book: A.F. Izmailov and M.V. Solodov.
``Numerical Methods of Optimization'',
Fizmatlit/Nauka, Moscow, Russia, 2003.
(In Russian, 304 pages).
  1.   Nonlinear complementarity as unconstrained and constrained minimization.

    2. O.L. Mangasarian and M.V. Solodov
    Mathematical Programming  62 (1993), 277-297.
    [ ps ] (Click herefor the title page)
     
  2.   Serial and parallel backpropagation convergence via nonmonotone perturbed minimization.

    3. O.L. Mangasarian and M.V. Solodov
    Optimization Methods and Software 4 (1994), 103-116.
    [ ps ]
     
  3.   New error bounds for the linear complementarity problems.

    4. Z.-Q. Luo, O.L. Mangasarian, J. Ren, and M.V. Solodov
    Mathematics of Operations Research 19 (1994), 880-892.
    [ ps ]
     
  4.   Backpropagation convergence via deterministic perturbed minimization.

    5. O.L. Mangasarian and M.V. Solodov
    In  Advances in Neural Information Processing Systems , Vol. 6, pp. 383-390,
    J.D. Cowan, G. Tesauro and J. Alspector (editors), Morgan Kaufmann Publishers, 1994.
    [ ps ]
     
  5.   Nonmonotone and Perturbed Optimization, Ph.D. Dissertation.

    6. M.V. Solodov
    Mathematical Programming Technical Report 95-13,
    Computer Sciences Department, University of Wisconsin,
    1210 West Dayton Street, Madison, Wisconsin 53706, U.S.A., August 1995.
     
  6.   Modified projection-type methods for monotone variational inequalities.

    7. M.V. Solodov and P. Tseng
    SIAM Journal on Control and Optimization 34(1996), 1814-1830.
    [ ps ]
     
  7.   New inexact parallel variable distribution algorithms.

    8. M.V. Solodov
    Computational Optimization and Applications 7 (1997), 165-182.
    [ ps ]
     
  8.   Convergence analysis of perturbed feasible descent methods.

    9. M.V. Solodov
    Journal of Optimization Theory and Applications 93 (1997), 337-353.
    [ ps ]
     
  9.   Minimization of nonsmooth convex functionals in Banach spaces.

    10. Ya.I. Alber, A.N. Iusem and M.V. Solodov
    Journal of Convex Analysis 4 (1997), 235-255.
    [ ps ]
     
  10.   Descent methods with linesearch in the presence of perturbations.

    11. M.V. Solodov and B.F. Svaiter
    Journal of Computational and Applied Mathematics 80 (1997), 265-275.
     
  11.   Newton-type methods with generalized distances for constrained optimization.

    12. A.N. Iusem and M.V. Solodov
    Optimization 41 (1997), 257-278.
    [ ps ]
     
  12.   Stationary points of bound constrained minimization reformulations of complementarity problems.

    13. M.V. Solodov
    Journal of Optimization Theory and Applications 94 (1997), 449-467.
    [ ps ]
     
  13.   On the convergence of constrained parallel variable distribution algorithms.

    14. M.V. Solodov
    SIAM Journal on Optimization 8 (1998), 187-196.
    [ ps ]
     
  14.   Error stability properties of generalized gradient-type algorithms.

    15. M.V. Solodov and S.K. Zavriev
    Journal of Optimization Theory and Applications 98 (1998), 663-680.
    [ ps ]
     
  15.   On the projected subgradient method for nonsmooth convex optimization in a Hilbert space.

    16. Ya.I. Alber, A.N. Iusem and M.V. Solodov
    Mathematical Programming 81 (1998), 23-35.
    [ ps ]
     
  16.   Incremental gradient algorithms with stepsizes bounded away from zero.

    17. M.V. Solodov
    Computational Optimization and Applications 11 (1998), 23-35.
    [ ps ]
     
  17.   A globally convergent inexact Newton method for systems of monotone equations.

    18. M.V. Solodov and B.F. Svaiter
    In  Reformulation - Nonsmooth, Piecewise Smooth, Semismooth and Smoothing Methods ,
    M. Fukushima and L. Qi (editors), Applied Optimization 22, Kluwer Academic Publishers, 1999,
    pp. 355-369.
    [ ps ]
     
  18.   Some optimization reformulations of the extended linear complementarity problem.

    19. M.V. Solodov
    Computational Optimization and Applications 13 (1999), 187-200.
    [ ps ]
     
  19.   A new projection method for variational inequality problems.

    20. M.V. Solodov and B.F. Svaiter
    SIAM Journal on Control and Optimization 37 (1999), 765-776.
    [ ps ]
     
  20.   Parallel constrained optimization via distribution of variables.

    21. C.A. Sagastizábal and M.V. Solodov
    In  Lecture Notes in Computer Science, Vol. 1685, pp. 1112-1119, P. Amestoy et al. (editors),
    Springer-Verlag, 1999.
     
  21.   A hybrid projection--proximal point algorithm.

    22. M.V. Solodov and B.F. Svaiter
    Journal of Convex Analysis 6 (1999), 59-70.
    [ ps ]
     
  22.   A projection-type method for pseudomonotone variational inequality problems.

    23. M.V. Solodov and B.F. Svaiter
    In  Proceedings of the 38-th IEEE Conference on Decision and Control, Omnipress, 1999, pp. 2569-2574.
     
  23.   A linearly convergent derivative-free descent method for strongly monotone complementarity problems.

    24. O.L. Mangasarian and M.V. Solodov
    Computational Optimization and Applications 14 (1999), 5-16.
    [ ps ]
     
  24.   A hybrid approximate extragradient--proximal point algorithm using the enlargement of a maximal monotone operator.

    25. M.V. Solodov and B.F. Svaiter
    Set-Valued Analysis 7 (1999), 323-345.
    [ ps ]
     
  25.   Globalization strategies in successive linearization methods for variational inequalities.

    26. M.V. Solodov
    In  Actas de VI Congreso de Matematica Aplicada, R. Montenegro, G. Montero and G. Winter (editors), Universidad de Las Palmas de Gran Canaria, 1999, pp. 1307-1314.
     
  26.   Forcing strong convergence of proximal point iterations in a Hilbert space.

    27. M.V. Solodov and B.F. Svaiter
    Mathematical Programming 87 (2000), 189-202.
    [ ps ]
     
  27.   A truly globally convergent Newton-type method for the monotone nonlinear complementarity problem.

    28. M.V. Solodov and B.F. Svaiter
    SIAM Journal on Optimization 10 (2000), 605-625.
    [ ps ]
     
  28.   The theory of 2-regularity for mappings with Lipschitz derivatives and its applications (a summary in Russian of papers 35 and 39 below).

    29. A.F. Izmailov and M.V. Solodov
    In  Problems of Modeling and Analysis in Decision Making Problems,
    V.A. Bereznev, V.G. Karmanov and A.A. Tretyakov (editors), Computing Center of the Russian Academy of Sciences, 2000, pp. 26-50.
    [ ps ]
     
  29.   An inexact hybrid generalized proximal point algorithm and some new results on the theory of Bregman functions.

    30. M.V. Solodov and B.F. Svaiter
    Mathematics of Operations Research 25 (2000), 214-230.
    [ ps ]
     
  30.   Some methods based on the D-gap function for solving monotone variational inequalities.

    31. M.V. Solodov and P. Tseng
    Computational Optimization and Applications 17 (2000), 255-277.
    [ ps ]
     
  31.   A comparison of rates of convergence of two inexact proximal point algorithms.

    32. M.V. Solodov and B.F. Svaiter
    In  Nonlinear Optimization and Related Topics,
    G. Di Pillo and F. Giannessi (editors), Applied Optimization 36, Kluwer Academic Publishers, 2000, pp. 415-427.
    [ ps ]
     
  32.   Error bounds for proximal point subproblems and associated inexact proximal point algorithms.

    33. M.V. Solodov and B.F. Svaiter
    Mathematical Programming 88 (2000), 371-389.
    [ ps ]
     
  33.   Implicit Lagrangian.

    34. M.V. Solodov
    An invited article for the Encyclopedia of Optimization, C. Floudas and P. Pardalos (editors),
    Kluwer Academic Publishers, 2001.
    [ ps ]
     
  34.   On the relation between bundle methods for maximal monotone inclusions and hybrid proximal point algorithms.

    35. C.A. Sagastizábal and M.V. Solodov
    In   Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications,
    D. Butnariu, Y. Censor and S. Reich (editors), Studies in Computational Mathematics 8, Elsevier Science B.V., 2001, pp. 441-455.
    [ ps ]
     
  35.   Error bounds for 2-regular mappings with Lipschitzian derivatives and their applications.

    36. A.F. Izmailov and M.V. Solodov
    Mathematical Programming 89 (2001), 413-435.
    [ ps ]
     
  36.   A class of globally convergent algorithms for pseudomonotone variational inequalities.

    37. M.V. Solodov
     In  Complementarity: Applications, Algorithms and Extensions,
    M C. Ferris, O.L. Mangasarian and J.-S. Pang (editors), Applied Optimization 50, Kluwer Academic Publishers, 2001, Chapter 14, pp. 297-315.
    [ ps ]
     
  37.   Optimality conditions for irregular inequality-constrained problems.

    38. A.F. Izmailov and M.V. Solodov
    SIAM Journal on Control and Optimization 40 (2001), 1280-1295.
    [ ps ]
     
  38.   A unified framework for some inexact proximal point algorithms.

    39. M.V. Solodov and B.F. Svaiter
    Numerical Functional Analysis and Optimization 22 (2001), 1013-1035.
    [ ps ]
     
  39.   The theory of 2-regularity for mappings with Lipschitzian derivatives and its applications to optimality conditions.

    40. A.F. Izmailov and M.V. Solodov
    Mathematics of Operations Research 27 (2002), 614-635.
    [ ps ]
     
  40.   Complementarity constraint qualification via the theory of 2-regularity.

    41. A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 13 (2002), 368-385.
    [ ps ]
     
  41.   Parallel variable distribution for constrained optimization.

    42. C.A. Sagastizábal and M.V. Solodov
    Computational Optimization and Applications 22 (2002), 111-131.
    [ ps ]
     
  42.   Superlinearly convergent algorithms for solving singular equations and smooth reformulations of complementarity problems.

    43. A.F. Izmailov and M.V. Solodov
    SIAM Journal on Optimization 13 (2002), 386-405.
    [ ps ]
     
  43.   A new proximal-based globalization strategy for the Josephy-Newton method for variational inequalities.

    44. M.V. Solodov and B.F. Svaiter
    Optimization Methods and Software 17 (2002), 965-983.
    [ ps ]
     
  44.   On optimality conditions for cone-constrained optimization. (a conference version of paper 37 above)

    45. A.F. Izmailov and M.V. Solodov
    In  Proceedings of the 41-st IEEE Conference on Decision and Control, Omnipress, 2002.
     
  45.   Convergence rate analysis of iterative algorithms for solving variational inequality problems.

    46. M.V. Solodov
    Mathematical Programming 96 (2003), 513-528.
    [ ps ]
     
  46.   Merit functions and error bounds for generalized variational inequalities.

    47. M.V. Solodov
    Journal of Mathematical Analysis and Applications 287 (2003), 405-414.
     
  47.   Karush-Kuhn-Tucker systems: regularity conditions, error bounds and a class of Newton-type methods.

    48. A.F. Izmailov and M.V. Solodov
    Mathematical Programming 95 (2003), 631-650.
    [ ps ]
     
  48.   On approximations with finite precision in bundle methods for nonsmooth optimization.

    49. M.V. Solodov
    Journal of Optimization Theory and Applications 119 (2003), 151-165.
    [ ps ]
     
  49.   On the sequential quadratically constrained quadratic programming methods.

    50. M.V. Solodov
    Mathematics of Operations Research 29 (2004), 64-79.
    [ pdf ]
     
  50.   Newton-type methods for optimization problems without constraint qualifications.

    51. A.F. Izmailov and M.V. Solodov
    May 2003 (Revised November 2003).
    To appear in SIAM Journal on Optimization.
    [ pdf ]
     
  51.   A class of active-set Newton methods for mixed complementarity problems.

    52. A.N. Daryina, A.F. Izmailov and M.V. Solodov
    IMPA preprint A256, October 2003.
    [ ps ]
     
  52.   A class of decomposition methods for convex optimization and monotone variational inclusions via the hybrid inexact proximal point framework.

    53. M.V. Solodov
    October 2003 (revised February 2004).
    To appear in Optimization Methods and Software.
    [ pdf ]
     
  53.   An infeasible bundle method for nonsmooth convex constrained optimization without a penalty function or a filter.

    54. C.A. Sagastizábal and M.V. Solodov
    IMPA preprint A273, February 2004.
    [ pdf ]
Last Updated: February 2004





EDUCATION:
Ph.D. in     Optimization/Computer Sciences from
University of Wisconsin - Madison, 1995.
(Advisor: Olvi L. Mangasarian,
John von Neumann Professor of Mathematics and Computer Sciences)

M.S.     (Computer Sciences)
University of Wisconsin - Madison, 1992.

Diploma     (with Honors, Applied Mathematics)
Moscow State University, 1991.


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